2 small lemons, cut into thin rounds
1 ½ teaspoons sugar
4 garlic cloves, halved
4 (6-ounce) skinless, boneless chicken breast halves, pounded to 3/4-inch thickness
½ teaspoon kosher salt, divided
½ teaspoon freshly ground black pepper
1 tablespoon olive oil, divided
2 tablespoons unsalted butter, divided
1 teaspoon grated shallot
½ teaspoon grated garlic
1 oregano sprig
1 thyme sprig
½ cup dry white wine
1 cup unsalted chicken stock (such as Swanson)
1 teaspoon all-purpose flour
1 tablespoon capers, rinsed and drained
2 tablespoons chopped fresh flat-leaf parsley
Combine lemon slices, sugar, and garlic in a medium bowl.
Sprinkle chicken with 3/8 teaspoon salt and pepper. Heat a large skillet over medium-high heat. Add 2 teaspoons oil; swirl to coat. Add chicken to pan; cook 4 minutes on each side or until done. Place chicken on a plate. Add remaining 1 teaspoon oil to pan; swirl to coat. Add lemon mixture to pan; cook 1 minute or until lemon slices are lightly browned, turning occasionally. Return lemon mixture to bowl.
Wipe pan with paper towels. Heat pan over medium heat. Add 1 1/2 teaspoons butter to pan; swirl until butter melts. Add shallot, 1/2 teaspoon grated garlic, oregano sprig, and thyme sprig; cook 1 minute. Add wine to pan, scraping pan to loosen browned bits. Bring to a boil; cook 3 minutes or until liquid almost evaporates. Add remaining 1/8 teaspoon salt, stock, and flour to pan, stirring with a whisk. Bring to a boil; reduce heat, and simmer 3 minutes or until liquid is reduced to about 2/3 cup. Remove pan from heat; discard oregano and thyme sprigs. Stir in remaining 1 1/2 tablespoons butter and capers, stirring until butter melts. Return chicken and any juices to pan; turn to coat with sauce. Top chicken with lemon mixture. Sprinkle with parsley.